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At the end of this module, students should be able to…
Explain the ways that molecular motion affect resulting NMR spectra (Scientific Ability A1)
Predict and test how NMR signal and frequency spectrum will differ from liquid and soft-solid samples (Scientific Abilities C4 and C8)
Identify challenges of solid-state NMR compared with liquid-state NMR (Scientific Ability A2)
“Rocks are the key to Earth history, because solids remember but liquids and gases forget.”
Example Real-World Application Solid-state NMR spectroscopy is a technique for characterizing chemical structure in solid materials like powders, single crystals, and tissues. Due to the limited molecular motion in the solid-state, clever strategies must be utilized to resolve the broad solid-state spectral peaks, including line-narrowing pulse sequences and magic angle spinning .
Image source (2) Featured Chemist Professor Dame Clare Grey is a chemist that uses solid-state NMR and other techniques to investigate local structure and physical properties of disordered materials such as those used in rechargeable batteries and supercapacitors. Read more about her work at https://www.ch.cam.ac.uk/person/cpg27.
Magnetic resonance techniques can technically work with any phase of matter, as long as the sample includes sub-atomic particles with non-zero quantum spin - which is certainly the vast majority of samples! However, liquid-state NMR spectroscopy is by far the most common, and in this module we will explore why that is the case. We will see how the microscopic differences in different states of matter can impact our MR signal and ultimately determine the challenges this poses for doing NMR and MRI on non-liquid samples.
To begin our exploration, let’s first discuss what we understand about what differentiates the three states of matter illustrated in the figure below.
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What are some key differences of the three states of matter depicted in the figure shown above?
Are there any important key differences in the three states of matter that you know about that are not depicted above?
How might you revise the figure above to include these other important key differences in the three states of matter?
Richard Ernst & Thomas Baumann in the lab, Photo: Private Archive Richard Ernst, featured in (4)
Richard Ernst - a Swiss physical chemist who was awarded the Chemistry Nobel Prize in 1991 for his contributions towards the development of Fourier transform nuclear magnetic resonance spectroscopy. It took several decades for the scientific community to recognize the significance of this work, as detailed in the quote below from his Nobel Prize Biographical.
“The response to our invention was however meager. The paper that described our achievements was rejected twice by the Journal of Chemical Physics to be finally accepted and published in the Review of Scientific Instruments. Varian also resisted to build a spectrometer that incorporated the novel Fourier transform concept. It took many years before in the competitive company Bruker Analytische Messtechnik Tony Keller and his coworkers demonstrated in 1969 for the first time a commercial FT NMR spectrometer to the great amazement of Varian that had the patent rights on the invention.” - Richard Ernst
One of the key differences between different states of matter is the relative motion of the atoms and molecules making up the sample. To develop a better idea of how the motion of atoms in the sample may ultimately impact our MR signal, let’s first observe how moving magnets with various amounts of motion can impact the magnetic field being measured at different locations in space.
To conduct these experiments, you will need:
- a handful of small compasses to serve as local magnetic field sensors
- a few small magnets who will act as our magnetic spins in the sample
The needle of each compass will align with the local magnetic field at the location of each compass. If the local magnetic field is homogeneous the compass needles located at different regions of space should all roughly be aligned, if the magnetic field is inhomogeneous, then the compass needles will be pointing in multiple directions.
Procedure
Set up a small grid of compasses separated by 3 - 4 inches in a location where the local magnetic field appears to be largely homogeneous - most likely the compasses are just aligning with the Earth’s magnetic field.
Randomly place the small magnets in and around the grid of compasses and keep the magnets stationary.
If you don’t have access to these materials, you can watch this video.
What phase of matter would be the closest analogue of this experimental setup?
How does the magnetic field appear to vary over different regions of space (i.e. is it more or less homogeneous than before the magnets were added)?
Would you expect a sample that is analogous to this experimental setup to have a long or short \(T_2\) relaxation time constant? Why?
Procedure
Multiple students should move the magnets around. This motion should include rotating the magnets along with moving the magnet around the region of space where the grid of compasses has been set up.
Other students observe the response of the compasses.
If you don’t have access to these materials, you can watch this video.
time-averaged - average value over a period of time
How does the time-averaged magnetic field appear to vary over different regions of space? Does it seem to depend on how fast the magnets are moving? How so?
Would you expect a sample that is analogous to this experimental setup to have a longer or shorter \(T_2\) relaxation time constant compared with Experiment 1? Why?
Based on the previous observation experiments, Alice and Sayed came up with the following hypothesis to explain how molecular motion may impact the \(T_2\) relaxation time:
Hypothesis: The faster the molecular motion in the sample, the more homogeneous the spin magnetic environments, and the longer the \(T_2\) relaxation time.
Design an experiment that can be used to test the hypothesis given above. Include a pulse sequence diagram and explain your choice in the timing values you would use (e.g. \(\tau\), TR, etc.)
For your designed experiment, what would you predict to see in the resulting time-domain signal if the hypothesis above is correct? Feel free to include rough sketches of your predictions!
Perform your experiment - or look at the provided experimental data that Alice and Sayed collected below - and use these results to make a reasonable judgment about the hypothesis.
molecular tumbling rate - how fast the molecules within the sample are moving around, with larger molecules and/or more solid samples having slower tumbling rates and smaller molecules and/or liquid samples having faster tumbling rates Below is a plot of what is generally found for \(T_1\) and \(T_2\) relaxation times for various molecular tumbling rates.
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Does the plot for the \(T_2\) relaxation time versus molecular “tumbling” rate match with your experimental conclusions?
Note that the correspondence of \(T_1\) in response to molecular “tumbling” rate is not quite as straightforward. It is actually minimal when the tumbling rate is equal to the Larmor frequency. Provide a possible explanation given what we know about resonance (e.g. that using resonance gives the most efficient energy transfer between systems) and the fact that \(T_1\) is related to the energy transfer between the environment and the quantum spins.
In the ideal MR experiments, we would have the longest possible T2 time - so our signal lasts longer and we get sharper spectral peaks - and the smallest possible T1 time - so we can repeat our experiments faster. Explain, using the diagram above, why solid-state NMR leads to un-ideal MR experiments.
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RECALL: How
does an exponential decay in the time-domain signal impact the Fourier
transform? As the signal decays faster (i.e. shorter \(T_2\)
relaxation time) what happens to the width of the peak in the frequency
spectrum? (Hint: See Module 8) 1. In MR experiments,
narrow peaks help both with detection sensitivity - signal strength -
and spectral resolution - how easy it is to see distinct, individual
peaks in the frequency spectrum. These both are very important for
identifying peaks in the frequency spectrum and having higher resolution
in imaging. One common way to get narrower peaks in solid-state NMR is
to do
magic
angle spinning, where the sample is spun at frequencies up to 130
kHz about an axis that is tilted at the magic angle 54.74\(^\circ\) with respect to the magnetic
field. The magic angle comes from the mathematical formula for the
spin-spin coupling causing the short \(T_2\) which is beyond the scope of this
module, but why might rotating the sample help narrow the spectral
peaks, given what you have learned in this module?
FUN FACT! Hyperpolarized gas MR imaging uses hyperpolarized helium and xenon gases as non-toxic, non-radioactive inhaled contrast agents that provide functional and structural information about the lungs that cannot be obtained using any other clinical imaging methods. For more information, check out (7).
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Looking at the table above, we see that water and cerebral spinal fluid has the longest \(T_2\) time out of the tissues listed. Using what you learned about molecular tumbling rate and its impact on the \(T_2\) relaxation time, explain why this makes sense.
In MR imaging (MRI), the brightness of the individual voxels (3D pixels) in the 3D image is related to the amount of MR signal one detects in that region of space along with how quickly that signal decays as the signal is being acquired. Suppose we were doing an \(^1\)H MRI of a human head, which has a layer of fat outside the skull and cerebral spinal fluid and gray matter inside. Which of these tissues would show up as the brightest voxels in the image (i.e. have the most signal)? Which of these tissues would show up as the darkest voxels?
Applications of solid state NMR: https://analyticalsciencejournals.onlinelibrary.wiley.com/doi/full/10.1002/mrc.5071 https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4413014/ https://pubs.acs.org/doi/10.1021/acs.analchem.2c02905#
Overview of NMR spectroscopy for solids: https://www.bruker.com/en/resources/library/application-notes-mr/nmr-spectroscopy-for-solids.html
Macromolecule effect on T1 and T2: https://mriquestions.com/macromolecule-effects.html
Molecular motion effect on T1 and T2: https://mriquestions.com/dipole-dipole-interactions.html https://mriquestions.com/bo-effect-on-t1–t2.html
